Using mathematics in MRI data management for glioma assesment.

Our aim is to review the mathematical tools usefulness in MR data management for glioma diagnosis and treatment optimization. MRI does not give access to organs variations in hours or days. However a lot of multiparametric data are generated. Mathematics could help to override this paradox, the aim of this article is to show how. We first make a review on mathematical modelling using equations. Afterwards we present statistical analysis. We provide detailed examples in both sections. We finally conclude, giving some clues on in silico models.

Analysis of a Mathematical Model for the Glutamate/Glutamine Cycle in the Brain.

Our aim in this article is to study the well-posedness and properties of a system with delay which is related with brain glutamate and glutamine kinetics. In particular, we prove the existence and uniqueness of nonnegative solutions. We also give numerical simulations and compare their order of magnitude with experimental data.

Added Value of Spectroscopy to Perfusion MRI in the Differential Diagnostic Performance of Common Malignant Brain Tumors.

BACKGROUND AND PURPOSE: Perfusion and spectroscopic MR imaging provide noninvasive physiologic and metabolic characterization of tissues, which can help in differentiating brain tumors. We investigated the diagnostic role of perfusion and spectroscopic MR imaging using individual and combined classifiers of these modalities and assessed the added performance value that spectroscopy can provide to perfusion using optimal combined classifiers that have the highest differential diagnostic performance to discriminate lymphomas, glioblastomas, and metastases. MATERIALS AND METHODS: From January 2013 to January 2016, fifty-five consecutive patients with histopathologically proved lymphomas, glioblastomas, and metastases were included after undergoing MR imaging. The perfusion parameters (maximum relative CBV, maximum percentage of signal intensity recovery) and spectroscopic concentration ratios (lactate/Cr, Cho/NAA, Cho/Cr, and lipids/Cr) were analyzed individually and in optimal combinations. Differences among tumor groups, differential diagnostic performance, and differences in discriminatory performance of models with quantification of the added performance value of spectroscopy to perfusion were tested using 1-way ANOVA models, receiver operating characteristic analysis, and comparisons between receiver operating characteristic analysis curves using a bivariate χ2, respectively. RESULTS: The highest differential diagnostic performance was obtained with the following combined classifiers: maximum percentage of signal intensity recovery-Cho/NAA to discriminate lymphomas from glioblastomas and metastases, significantly increasing the sensitivity from 82.1% to 95.7%; relative CBV-Cho/NAA to discriminate glioblastomas from lymphomas and metastases, significantly increasing the specificity from 92.7% to 100%; and maximum percentage of signal intensity recovery-lactate/Cr and maximum percentage of signal intensity recovery-Cho/Cr to discriminate metastases from lymphomas and glioblastomas, significantly increasing the specificity from 83.3% to 97.0% and 100%, respectively. CONCLUSIONS: Spectroscopy yielded an added performance value to perfusion using optimal combined classifiers of these modalities, significantly increasing the differential diagnostic performances for these common brain tumors.

Low-grade gliomas: the challenges of imaging.

WHO grade II gliomas are a major challenge for magnetic resonance imaging (MRI) due to their delayed anaplastic transformation. Today it is possible to individually characterize tumor progression from diagnosis to anaplastic transformation based on the many parameters identified in studies in the literature and the possibility of integrating these data into mathematical models. Early identification of negative morphological and metabolic factors, as well as treatment follow-up, help identify predictive factors of tumor progression, as well as determine treatment response to adapt management of this disease.